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题目(2016年四川高考题)已知椭圆E:x~2/a~2+y~2/b~2=1(a>b>0)的一个焦点与短轴的两个端点是正三角形的三个顶点,点P(3~(1/2),12)在椭圆上.(1)求椭圆E的方程.(2)设不过原点O且斜率为1/2的直线l与椭圆E交于不同的两点A,B,线段AB的中点为M,直线OM与椭圆E交于C,D,求证:MA·MB=MC·MD.这是一道文科数学高考题,第(2)问表述非常平和朴实,亲切自然,以学生熟悉的直线和椭圆相交为载体,考查椭圆中相关问题的证明.着重考查学生对解析几何本质的理解,
Subject (2016 Sichuan Entrance Examination) It is known that the two endpoints of a focal point and a minor axis of an ellipse E: x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0) Three vertices, the point P (3 ~ (1/2), 12) on the ellipse. (1) Seek the equation of the ellipse E. (2) Let the intersection of the origin O and the slope of 1/2 straight line l and the intersection of the ellipse E At different points A, B, the middle point of the line segment AB is M, and the line OM intersects with the ellipse E at C, D. This verifies: MA · MB = MC · MD. Asked very calm and plain, natural and familiar to the students straight line and ellipse intersect as a carrier to test the relevant issues in the oval proof.Considered to examine students’ understanding of the nature of analytical geometry,